Question

Consider the diagram in the picture.

In order to set up a rowing competition, the crew needs to find a practice course in the lake. Using the diagram in the picture, determine which of the following reasons allows us to conclude that ‘x’ is equal to the distance across the lake.

(A) All three angles of the triangles are congruent, so the triangles must also be congruent.
(B) The triangles for two parallel lines; therefore, they must be congruent.
(C) Vertical angles are congruent, so by ASA, the two triangles are congruent.
(D) Alternate interior angles are congruent, so all of the sides must also be congruent.

Answer 1

C

Explanation:

Answer 2

(C) Vertical angles are congruent, so by ASA, the two triangles are congruent.

Explanation:

The Angle-Side-Angle Postulate (ASA) tells us that if triangles have matching angles and a matching side length between the angles, they're definitely congruent. From the graph, we have one matching side and one matching angle. Since the side that measures 1000m and the other side that measures 2095.2m intersect, then at this point we have vertical angles and those types of angles are always congruent. Therefore, we have now two corresponding angles that are congruent and one corresponding side that is congruent. So we can apply ASA postulate.